Article

Quasi-proportional mechanisms: prior-free revenue maximization

Authors:

Vahab Mirrokni,

S. Muthukrishnan,

Uri NadavAuthors Info & Claims

LATIN'10: Proceedings of the 9th Latin American conference on Theoretical Informatics

Pages 565 - 576

https://doi.org/10.1007/978-3-642-12200-2_49

Published: 19 April 2010 Publication History

Abstract

Inspired by Internet ad auction applications, we study the problem of allocating a single item via an auction when bidders place very different values on the item. We formulate this as the problem of prior-free auction and focus on designing a simple mechanism that always allocates the item. Rather than designing sophisticated pricing methods like prior literature, we design better allocation methods. In particular, we propose quasi-proportional allocation methods in which the probability that an item is allocated to a bidder depends (quasi-proportionally) on the bids.

We prove that corresponding games for both all-pay and winners-pay quasi-proportional mechanisms admit pure Nash equilibria and this equilibrium is unique. We also give an algorithm to compute this equilibrium in polynomial time. Further, we show that the revenue of the auctioneer is promisingly high compared to the ultimate, i.e., the highest value of any of the bidders, and show bounds on the revenue of equilibria both analytically, as well as using experiments for specific quasi-proportional functions. This is the first known revenue analysis for these natural mechanisms (including the special case of proportional mechanism which is common in network resource allocation problems).

References

[1]

Abernethy, J., Hazan, E., Rakhlin, A.: Competing in the Dark: An Efficient Algorithm for Bandit Linear Optimization. In: COLT 2008 (2008).

[2]

Baliga, S., Vohra, R.: Market Research and Market Design (2003).

[3]

Baye, M., Kovenock, D., de Vried, C.: The all-pay auction with Complete Information. Economic Theory 8, 291-305.

[4]

Che, Y., Gale, I.: Expected revenue of all-pay auctions and first-price sealed-bid auctions with budget constraints. Economic Letters, 373-379 (1996).

[5]

Clarke, E.: Multipart pricing of public goods. Public Choice 11, 17-33 (1971).

[6]

Even Dar, E., Mansour, Y., Nadav, U.: On the convergence of regret minimization dynamics in concave games. In: STOC 2009 (2009).

Digital Library

[7]

Fiat, A., Goldberg, A.V., Hartline, J.D., Karlin, A.R.: Competitive generalized auctions. In: STOC 2002, pp. 72-81 (2002).

Digital Library

[8]

Groves, T.: Incentives in teams. Econometrica 41(4), 617-631 (1973).

[9]

Hajek, B., Gopalakrishnan, G.: Do greedy autonomous systems make for a sensible internet? Presented at the Conference on Stochastic Networks, Stanford University (2002).

[10]

Hartline, J., Karline, A.: Profit Maximization in Mechanism Design. In: Algorithmic Game Theory (October 2007).

[11]

Johari, R., Tsitsiklis, J.N.: Efficiency loss in a network resource allocation game. Mathematics of Operations Research 29(3), 407-435 (2004).

Digital Library

[12]

Kalai, A., Vempala, S.: Efficient algorithms for online decision problems. J. Comput. Syst. Sci. 71(3), 291-307 (2005).

Digital Library

[13]

Kelly, F.: Charging and rate control for elastic traffic. European Transactions on Telecommunications 8, 33-37 (1997).

[14]

Liu, D., Chen, J.: Designing online auctions with past performance information. Decision Support Systems 42, 1307-1320 (2006).

Digital Library

[15]

Lu, P., Teng, S.-H., Yu, C.: Truthful Auctions with Optimal Profit. In: Spirakis, P.G., Mavronicolas, M., Kontogiannis, S.C. (eds.) WINE 2006. LNCS, vol. 4286, pp. 27-36. Springer, Heidelberg (2006).

Digital Library

[16]

Myerson, R.: Optimal auction design. Mathematics of Operations Research 6, 58-73 (1981).

Digital Library

[17]

Rosen, J.: Existence and uniqueness of equilibrium points for concave n-person games. Econometrica, 520-534 (1965).

[18]

Segal, I.: Optimal Pricing Mechanisms with Unknown Demand. American Economic Review 93(3), 509-529 (2003).

[19]

Vickrey, W.: Counterspeculation, auctions and competitive-sealed tenders. Finance 16(1), 8-37 (1961).

[20]

Zinkevich, M.: Online convex programming and generalized infinitesimal gradient ascent. In: Twentieth International Conference on Machine Learning (2003).

Digital Library

Cited By

Liaw CMehta AZhu WChua TNgo CKa-Wei Lee RKumar RLauw H(2024)Efficiency of Non-Truthful Auctions in Auto-bidding with Budget ConstraintsProceedings of the ACM Web Conference 202410.1145/3589334.3645636(223-234)Online publication date: 13-May-2024
https://dl.acm.org/doi/10.1145/3589334.3645636
Fotakis DTsipras DTzamos CZampetakis E(2016)Efficient Money Burning in General DomainsTheory of Computing Systems10.1007/s00224-016-9720-259:4(619-640)Online publication date: 1-Nov-2016
https://dl.acm.org/doi/10.1007/s00224-016-9720-2

Quasi-proportional mechanisms: prior-free revenue maximization
1. Applied computing
  1. Law, social and behavioral sciences
2. Theory of computation

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Published In

cover image Guide Proceedings

LATIN'10: Proceedings of the 9th Latin American conference on Theoretical Informatics

April 2010

712 pages

ISBN:3642121993

Editor:
Alejandro López-Ortiz
Faculty of Mathematics, Department of Computer Science, University of Waterloo, Waterloo, Ontario, Canada

Sponsors

UWATERLOO: University of Waterloo
Yahoo! Research
Microsoft Research: Microsoft Research
Benito Juárez University of Oaxaca: Benito Juárez University of Oaxaca

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Springer-Verlag

Berlin, Heidelberg

Publication History

Published: 19 April 2010

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Cited By

Liaw CMehta AZhu WChua TNgo CKa-Wei Lee RKumar RLauw H(2024)Efficiency of Non-Truthful Auctions in Auto-bidding with Budget ConstraintsProceedings of the ACM Web Conference 202410.1145/3589334.3645636(223-234)Online publication date: 13-May-2024
https://dl.acm.org/doi/10.1145/3589334.3645636
Fotakis DTsipras DTzamos CZampetakis E(2016)Efficient Money Burning in General DomainsTheory of Computing Systems10.1007/s00224-016-9720-259:4(619-640)Online publication date: 1-Nov-2016
https://dl.acm.org/doi/10.1007/s00224-016-9720-2

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